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Maximal Rigid Objects as Noncrossing Bipartite Graphs

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Abstract

We classify the maximal rigid objects of the Σ2 τ-orbit category \({\mathcal{C}}(Q)\) of the bounded derived category for the path algebra associated to a Dynkin quiver Q of type A, where τ denotes the Auslander-Reiten translation and Σ2 denotes the square of the shift functor, in terms of bipartite noncrossing graphs (with loops) in a circle. We describe the endomorphism algebras of the maximal rigid objects, and we prove that a certain class of these algebras are iterated tilted algebras of type A.

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Authors and Affiliations

  1. School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    Raquel Coelho Simões

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  1. Raquel Coelho Simões
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Correspondence to Raquel Coelho Simões.

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Coelho Simões, R. Maximal Rigid Objects as Noncrossing Bipartite Graphs. Algebr Represent Theor 16, 1243–1272 (2013). https://doi.org/10.1007/s10468-012-9355-1

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  • DOI: https://doi.org/10.1007/s10468-012-9355-1

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